Learning the Sampling Pattern for MRI

TL;DR

This paper introduces a supervised learning framework to optimize MRI sampling patterns, achieving high-quality reconstructions with significantly reduced data acquisition by learning from limited training data.

Contribution

It presents a novel method for learning arbitrary MRI sampling patterns using minimal training data, improving acquisition efficiency without sacrificing image quality.

Findings

Learned sampling pattern samples only 35% of k-space.

Achieves mean SSIM of 0.914 on test images.

Effective with as few as 7 training pairs.

Abstract

The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long acquisition times can limit its use. In this work, we consider the problem of learning a sparse sampling pattern that can be used to optimally balance acquisition time versus quality of the reconstructed image. We use a supervised learning approach, making the assumption that our training data is representative enough of new data acquisitions. We demonstrate that this is indeed the case, even if the training data consists of just 7 training pairs of measurements and ground-truth images; with a training set of brain images of size 192 by 192, for instance, one of the learned patterns samples only 35% of k-space, however results in reconstructions with mean SSIM 0.914 on a test set of similar images. The proposed framework is general enough to learn arbitrary sampling patterns, including common patterns such as Cartesian, spiral and radial sampling.

Full text

Supporting document for "Learning the Sampling Pattern for MRI"

Ferdia Sherry, Martin Benning, Juan Carlos De los Reyes, Martin J. Graves, Georg Maierhofer, Guy Williams, Carola-Bibiane Schönlieb and Matthias J. Ehrhardt

S-I The test set

Figure 13 shows some of the variety in the images that were used to test the learned patterns.

S-II Varying the sparsity parameter $\beta$

Figure 14 shows slices through Gaussian kernel density estimates of the sampling distributions in Figure 4 in the main text.

S-III Varying the size of the training set

Figure 15 shows the learned patterns for each of the training set sizes investigated in Section III-E of the main text. It can be seen that the patterns become more strongly peaked around the centre of k-space as the size of the training set increases.

S-IV Training set for high resolution example

In the high resolution example of Section LABEL:sec:hires_example of the main text, we used the slices shown in Figure 16 for the training set.

S-V Convergence of L-BFGS-B for the upper level problem

The plots in Figure 17 show the evolution of the (normalised) objective function value with the iteration number for some of the experiments in Section LABEL:sec:vary_beta of the main text.